Ebook: Brain Dynamics: Synchronization and Activity Patterns in Pulse-Coupled Neural Nets with Delays and Noise
- Tags: Psychiatry, Biophysics/Biomedical Physics, Neurosciences, Complexity, Computational Mathematics and Numerical Analysis
- Series: Springer Series in Synergetics
- Year: 2007
- Publisher: Springer Berlin Heidelberg
- Language: English
- pdf
This book addresses a large variety of models in mathematical and computational neuroscience. It is written for the experts as well as for graduate students wishing to enter this fascinating field of research. The author studies the behaviour of large neural networks composed of many neurons coupled by spike trains. He devotes the main part to the synchronization problem. He presents neural net models more realistic than the conventional ones by taking into account the detailed dynamics of axons, synapses and dendrites, allowing rather arbitrary couplings between neurons. He gives a complete stabile analysis that goes significantly beyond what has been known so far. He also derives pulse-averaged equations including those of the Wilson--Cowan and the Jirsa-Haken-Nunez types and discusses the formation of spatio-temporal neuronal activity pattems. An analysis of phase locking via sinusoidal couplings leading to various kinds of movement coordination is included.
This book addresses a large variety of models in mathematical and computational neuroscience. It is written for the experts as well as for graduate students wishing to enter this fascinating field of research. The author studies the behaviour of large neural networks composed of many neurons coupled by spike trains. He devotes the main part to the synchronization problem. He presents neural net models more realistic than the conventional ones by taking into account the detailed dynamics of axons, synapses and dendrites, allowing rather arbitrary couplings between neurons. He gives a complete stabile analysis that goes significantly beyond what has been known so far. He also derives pulse-averaged equations including those of the Wilson--Cowan and the Jirsa-Haken-Nunez types and discusses the formation of spatio-temporal neuronal activity pattems. An analysis of phase locking via sinusoidal couplings leading to various kinds of movement coordination is included.
Content:
Front Matter....Pages I-XII
Front Matter....Pages 1-1
Introduction....Pages 3-7
The Neuron — Building Block of the Brain....Pages 9-16
Neuronal Cooperativity....Pages 17-36
Spikes, Phases, Noise: How to Describe Them Mathematically? We Learn a Few Tricks and Some Important Concepts....Pages 37-73
Front Matter....Pages 75-75
The Lighthouse Model. Two Coupled Neurons....Pages 77-101
The Lighthouse Model. Many Coupled Neurons....Pages 103-139
Integrate and Fire Models (IFM)....Pages 141-150
Many Neurons, General Case, Connection with Integrate and Fire Model....Pages 151-179
Front Matter....Pages 181-181
Phase Locking via Sinusoidal Couplings....Pages 183-194
Pulse-Averaged Equations....Pages 195-213
Front Matter....Pages 215-215
The Single Neuron....Pages 217-224
Conclusion and Outlook....Pages 225-227
Back Matter....Pages 229-248
This book addresses a large variety of models in mathematical and computational neuroscience. It is written for the experts as well as for graduate students wishing to enter this fascinating field of research. The author studies the behaviour of large neural networks composed of many neurons coupled by spike trains. He devotes the main part to the synchronization problem. He presents neural net models more realistic than the conventional ones by taking into account the detailed dynamics of axons, synapses and dendrites, allowing rather arbitrary couplings between neurons. He gives a complete stabile analysis that goes significantly beyond what has been known so far. He also derives pulse-averaged equations including those of the Wilson--Cowan and the Jirsa-Haken-Nunez types and discusses the formation of spatio-temporal neuronal activity pattems. An analysis of phase locking via sinusoidal couplings leading to various kinds of movement coordination is included.
Content:
Front Matter....Pages I-XII
Front Matter....Pages 1-1
Introduction....Pages 3-7
The Neuron — Building Block of the Brain....Pages 9-16
Neuronal Cooperativity....Pages 17-36
Spikes, Phases, Noise: How to Describe Them Mathematically? We Learn a Few Tricks and Some Important Concepts....Pages 37-73
Front Matter....Pages 75-75
The Lighthouse Model. Two Coupled Neurons....Pages 77-101
The Lighthouse Model. Many Coupled Neurons....Pages 103-139
Integrate and Fire Models (IFM)....Pages 141-150
Many Neurons, General Case, Connection with Integrate and Fire Model....Pages 151-179
Front Matter....Pages 181-181
Phase Locking via Sinusoidal Couplings....Pages 183-194
Pulse-Averaged Equations....Pages 195-213
Front Matter....Pages 215-215
The Single Neuron....Pages 217-224
Conclusion and Outlook....Pages 225-227
Back Matter....Pages 229-248
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